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arXiv · 2011.06370

Pointwise convergence of certain continuous-time double ergodic averages

Michael Christ·Polona Durcik·Vjekoslav Kovač·Joris Roos
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Abstract

We prove a.e. convergence of continuous-time quadratic averages with respect to two commuting $\mathbb{R}$-actions, coming from a single jointly measurable measure-preserving $\mathbb{R}^2$-action on a probability space. The key ingredient of the proof comes from recent work on multilinear singular integrals; more specifically, from the study of a curved model for the triangular Hilbert transform.

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Michael Christ, Polona Durcik, Vjekoslav Kovač, Joris Roos. 2020-11-12. Pointwise convergence of certain continuous-time double ergodic averages. https://doi.org/10.1017/etds.2021.45

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